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 Sibirsk. Mat. Zh., 2012, Volume 53, Number 1, Pages 89–106 (Mi smj2291)

The spaces of meromorphic Prym differentials on a finite Riemann surface

A. A. Kazantsevaa, V. V. Chueshevb

a Gorno-Altaisk State University, Faculty of Mathematics, Gorno-Altaisk
b Kemerovo State University, Faculty of Mathematics, Kemerovo

Abstract: In the previous articles the second author started constructing a general theory of multiplicative functions and Prym differentials on a compact Riemann surface for arbitrary characters. Function theory on compact Riemann surfaces differs substantially from that on finite Riemann surfaces. In this article we start constructing a general function theory on variable finite Riemann surfaces for multiplicative meromorphic functions and differentials. We construct the forms of all elementary Prym differentials for arbitrary characters and find the dimensions of, and also construct explicit bases for, two important quotient spaces of Prym differentials. This yields the dimension of and a basis for the first holomorphic de Rham cohomology group of Prym differentials for arbitrary characters.

Keywords: Teichmüller space of finite Riemann surfaces, Prym differential, vector bundle, character group, Jacobian variety, multiplicative Weierstrass point.

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English version:
Siberian Mathematical Journal, 2012, 53:1, 72–86

Bibliographic databases:

Document Type: Article
UDC: 515.17+517.545

Citation: A. A. Kazantseva, V. V. Chueshev, “The spaces of meromorphic Prym differentials on a finite Riemann surface”, Sibirsk. Mat. Zh., 53:1 (2012), 89–106; Siberian Math. J., 53:1 (2012), 72–86

Citation in format AMSBIB
\Bibitem{KazChu12} \by A.~A.~Kazantseva, V.~V.~Chueshev \paper The spaces of meromorphic Prym differentials on a~finite Riemann surface \jour Sibirsk. Mat. Zh. \yr 2012 \vol 53 \issue 1 \pages 89--106 \mathnet{http://mi.mathnet.ru/smj2291} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2962191} \transl \jour Siberian Math. J. \yr 2012 \vol 53 \issue 1 \pages 72--86 \crossref{https://doi.org/10.1134/S0037446612010065} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000303357700006} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84857547264} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. O. A. Sergeeva, “The Poincare Series and Operators of Duality for Multiplicative Automorphic Forms”, J. Math. Sci., 205:3 (2015), 445–454
2. M. I. Tulina, “Single-valued differentials and special divisors of Prym differentials”, Siberian Math. J., 54:4 (2013), 731–745
3. M. I. Tulina, V. V. Chueshev, “Prym Differentials on a Variable Compact Riemann Surface”, Math. Notes, 95:3 (2014), 418–433
4. A. A. Kazanceva, “Single-Valued $q$-Differentials on Variable Finite Riemann Surface”, J. Math. Sci., 213:6 (2016), 857–867
5. O. A. Chuesheva, “Prym differentials with matrix characters on a finite Riemann surface”, Siberian Math. J., 56:3 (2015), 549–556
6. E. V. Semenko, “Prym differentials as solutions to boundary value problems on Riemann surfaces”, Siberian Math. J., 57:1 (2016), 124–134
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